Resonant acoustic determination of complex elastic moduli

Abstract

An acoustic resonance based technique using a free-free bar has been extended to investigate the complex (storage and loss) moduli of non-magnetic materials having circular cross section. Using this technique, the bar can be selectively excited in three independent vibrational modes, i.e. torsional, flexural and longitudinal modes. The torsional mode yields the shear modulus. Either the flexural or longitudinal mode can be used to obtain Young's modulus. These resonant modes can be tracked continuously by means of a phase-locked-loop (PLL) as the temperature (and resonant frequency) of the rod is changed. The in-phase amplitude of the receiver output of the electrodynamic transducer is proportional to the quality factor,Q, of the material. It can be used to continuously track the loss tangent (=1/Q) of the material as a function of temperature and frequency. Results for complex shear modulus and Young's modulus were obtained for a castable epoxy type PR1592 and complex shear modulus for polymethyl methacrylate (PMMA) and Uralite 3130. Over the temperature and frequency range that was accessible, a clear viscoelastic transition was observed in both the storage modulus and loss tangent curves of PR1592.